Read the given instructions carefully and answer the related questions: Six…
2025
Read the given instructions carefully and answer the related questions:
Six persons – A, B, C, D, E and F – bought six different types of cars – Sedan, SUV, Hatchback, Limousine, Coupe, and Convertible – one after the other, but not necessarily in the same order. The one who bought Sedan purchased it three persons before F. As many persons bought car before F as after the one who purchased Hatchback. Two persons bought cars between the ones who purchased Hatchback and SUV. E bought the car before the one who purchased SUV but immediately before A. Coupe was bought two persons after A but immediately bought before convertible. Convertible was bought before B but after D.
Who bought the car three persons after that person who bought the car immediately before D?
- A.
C
- B.
B
- C.
F
- D.
A
- E.
None
Attempted by 10 students.
Show answer & explanation
Correct answer: A
Concept
In a linear arrangement puzzle, six people are placed in a fixed left-to-right order of action (here, the order of purchase, positions 1 to 6). The method is to convert each clue into a positional constraint, list the candidate placements each clue allows, and then intersect the clues until exactly one ordering survives. "X bought three persons before Y" means there are two people between them, i.e. position(X) + 3 = position(Y); "two persons between P and Q" means |position(P) - position(Q)| = 3.
Applying the clues
"As many persons bought a car before F as after the one who bought Hatchback" means position(F) - 1 = 6 - position(Hatchback), so position(F) + position(Hatchback) = 7. "The Sedan buyer purchased three persons before F" adds position(Sedan) + 3 = position(F). Together these leave two candidate pairs: F at position 4 with Hatchback at 3 (Sedan at 1), or F at position 6 with Hatchback at 1 (Sedan at 3).
"Two persons bought cars between Hatchback and SUV" gives |position(Hatchback) - position(SUV)| = 3. "E bought before the SUV buyer but immediately before A" requires the E-A block to sit left of SUV. Test the F-at-6 branch: Hatchback at 1, SUV at 4; then Coupe = position(A) + 2 with Convertible right after, and Convertible after D but before B cannot be fitted without a clash, so this branch is discarded.
That leaves the surviving branch: Sedan at 1, Hatchback at 3, F at 4, and SUV at 6 (three places from Hatchback).
Place the E-A block: "Coupe two persons after A and immediately before Convertible" with E immediately before A. Putting E at 1 and A at 2 makes Coupe position 4 and Convertible position 5, the only seating that keeps Convertible immediately after Coupe and left of SUV.
"Convertible was bought before B but after D": Convertible sits at position 5, so D precedes it and B follows. The two remaining people fall into positions 3 and 6, fixing D at 3 and B at 6.
Final arrangement
Position | Person | Car |
|---|---|---|
1 | E | Sedan |
2 | A | Limousine |
3 | D | Hatchback |
4 | F | Coupe |
5 | C | Convertible |
6 | B | SUV |
Answering the question
The question asks for the person three persons after the one who bought immediately before D. D is at position 3, so the buyer immediately before D is at position 2, namely A. Three persons after position 2 is position 5, which is C. Hence the required person is C.
Cross-check
Re-test the anchors on this ordering: Sedan (position 1) is exactly three places before F (position 4); persons before F = 3 equals persons after Hatchback at position 3 = 3; Hatchback (3) and SUV (6) have two buyers between them; Coupe (4) is two after A (2) and immediately before Convertible (5); Convertible (5) lies after D (3) and before B (6). Every clue holds, confirming C.